Femtoscopic correlations of identical charged pions and kaons in pp collisions at √s=13 TeV with event-shape selection

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Femtoscopic correlations of identical charged pions and kaons in pp collisions at √s=13 TeV with event-shape selection © 2024 CERN Published version ALICE collaboration ALICE collaboration. (2024). Femtoscopic correlations of identical charged pions and kaons in pp collisions at √s=13 TeV with event-shape selection. Physical Review C, 109(2), Article 024915. https://doi.org/10.1103/PhysRevC.109.024915 2024 PHYSICAL REVIEW C 109, 024915 (2024) Femtoscopic correlations of identical charged pions and kaons in pp collisions at √s=13 TeV with event-shape selection S. Acharya et al.∗ (ALICE Collaboration) (Received 17 October 2023; accepted 23 January 2024; published 23 February 2024) Collective behavior has been observed in high-energy heavy-ion collisions for several decades. Collectivity is driven by the high particle multiplicities that are produced in these collisions. At the CERN Large Hadron Collider (LHC), features of collectivity have also been seen in high-multiplicity proton-proton collisions that can attain particle multiplicities comparable to peripheral Pb-Pb collisions. One of the possible signatures of collective behavior is the decrease of femtoscopic radii extracted from pion and kaon pairs emitted from highmultiplicity collisions with increasing pair transverse momentum. This decrease can be described in terms of an approximate transverse mass scaling. In the present work, femtoscopic analyses are carried out by the ALICE Collaboration on charged pion and kaon pairs produced in pp collisions at √s=13 TeV from the LHC to study possible collectivity in pp collisions. The event-shape analysis method based on transverse sphericity is used to select for spherical versus jetlike events, and the effects of this selection on the femtoscopic radii for both charged pion and kaon pairs are studied. This is the first time this selection method has been applied to charged kaon pairs. An approximate transverse-mass scaling of the radii is found in all multiplicity ranges studied when the difference in the Lorentz boost for pions and kaons is taken into account. This observation does not support the hypothesis of collective expansion of hot and dense matter that should only occur in high-multiplicity events. A possible alternate explanation of the present results is based on a scenario of common emission conditions for pions and kaons in pp collisions for the multiplicity ranges studied. DOI: 10.1103/PhysRevC.109.024915 I. INTRODUCTION The manifestation of collective effects in pp (pp) and p-A collisions with increasing multiplicity of charged particles is intensely discussed in the literature [1–4]. Surprisingly, these small colliding systems exhibit several signatures attributed to the formation of a strongly interacting quark-gluon plasma in heavy-ion collisions, such as long-range ridgelike structures [5–7] and strangeness enhancement [8]. A full understanding of the mechanisms leading to collective effects observed in pp collisions at large multiplicity has not yet been achieved. For this reason, it is important to experimentally investigate the properties of small systems with the aim to discriminate between different theoretical models. Namely, the hydrodynamic models present the “heavy-ion view” of pp collisions, e.g., Ref. [9], while string models are the “high-energy view,” e.g., models including interactions between strings [10,11]. The femtoscopy technique, which studies the final-state hadron-hadron interactions via their momentum correlations, is an effective tool for the extraction of the space-time charac- ∗Full author list given at the end of the article. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by CERN. teristics of particle production processes, in particular the radii of the emitting source and the decoupling time. This method has already been employed in the past to study high-energy hadron-hadron [12,13] and heavy-ion collisions [14,15]using quantum statistical (QS) correlations and/or final-state interactions (FSI) of particles emitted with small relative momenta. The characteristic feature of femtoscopy in heavy-ion collisions is the decrease of the source sizes for pairs of particles (with masses mand transverse momenta pT,1and pT,2) with increasing pair transverse momentum kT=|pT,1+pT,2|/2or transverse mass mT=kT2+m2; see, e.g., recent results for pions from the BNL Relativistic Heavy Ion Collider (RHIC) [16–18] and the CERN Large Hadron Collider (LHC) [19,20]. It was explained in Ref. [21] that femtoscopy measurements do not probe the whole volume in the case of an expanding emitting source, but instead the region from which the particles with similar momenta are emitted, the so-called homogeneity volume. This region is smaller than the total volume occupied by the system and decreases with kT(mT). Several theoretical models based on the hydrodynamic approach successfully describe pion femtoscopy measurements, e.g., Refs. [22–26]. It is expected that these models should describe the femtoscopy measurements for kaons and for heavier particles also, particularly the mTand multiplicity dependencies of radii. In Ref. [27], it was shown that for the particular case of small transverse flow the hydrodynamics leads to the same mTbehavior of the longitudinal 2469-9985/2024/109(2)/024915(21) 024915-1 ©2024 CERN, for the ALICE Collaboration S. ACHARYA et al. PHYSICAL REVIEW C 109, 024915 (2024) radii (Rlong) for pions and kaons. It means that the thermal freeze-out occurs simultaneously and that these two particle species are subject to the same velocity boost from collective flow. Modern calculations made within the 3+1-dimensional (3+1D) hydrodynamic model THERMINATOR-2 [24]atLHC energies demonstrate the approximate mTscaling of the threedimensional radii for pions, kaons, and protons [26] when the radii versus mTfall with some degree of accuracy on one curve. The authors of Ref. [26] also investigated onedimensional radii (Rinv) in the pair reference frame (PRF) for the case of lack of available experimental data. They have verified that the violation of this scaling in the case when the three-dimensional scaling is presented in the model has a trivial kinematic origin. It is possible to take it into account and restore the mTscaling for Rinv for pions, kaons, and protons. The calculations performed within the hydrokinetic model, including not only a hydrodynamic phase but also the hadronic rescattering stage, predicted violation of this scaling between pions and kaons at LHC energies [28,29], mainly due to the rescatterings in the hadronic phase. ALICE results for Pb-Pb collisions at √sNN =2.76 TeV [30] have shown that the mTscaling expected by pure hydrodynamical scenarios is broken. The comparison of these two different evolution scenarios demonstrate the importance of the mTscaling study. At the LHC, the femtoscopic sizes range for various colliding systems from 2–7 fm for Pb-Pb to 1–2 fm for pp and p-Pb collisions, which opens a possible access to different energy densities of the system created during such collisions and probably helps us understand the conditions required for the QGP formation. The multiplicity and mTdependencies were studied for pions and kaons by ALICE for Pb-Pb collisions (e.g., Refs. [20,30]) and for pp and p-Pb collisions (e.g., Refs. [31–36]). In ppcollisions, it was observed for both types of pairs that for higher charged-particle multiplicity ranges the measured size of the source decreased with increasing mT, similarly to the trend seen in heavy-ion collisions. Instead, at low charged-particle multiplicities, the measured source radii increased with increasing mT[31,33,34]. Unfortunately, there are almost no theoretical models for pp collisions which include the space-time coordinates and can be used to describe femtoscopic observables. Attempts to describe the behavior of femtoscopic radii in pp collisions at the LHC from the hydrodynamic point of view were performed in, e.g., Refs. [37,38], from the view of the uncertainty principle in Ref. [39], and from the view of the string models in Ref. [40]usingthe Lund hadronization scheme which automatically introduces the space-momentum correlations, similar to the correlations in hydrodynamic models, where they arise due to transverse collective flow. The study of femtoscopic correlations in pp collisions is more challenging than in A-Acollisions due to the strong nonfemtoscopic contributions, i.e., correlations due to multibody resonance decays, minijets, and energy-momentum conservation. Typically, a baseline distribution function is constructed to remove these non femtoscopic effects, after which the hadron-hadron correlations due to pure QS and FSI can be studied. There are various methods to exclude them: (1) the “double ratio” technique, dividing the experimental correlation function by the baseline extracted from Monte Carlo simulations [31]; (2) the “cluster subtraction” technique, using the opposite-sign pair (e.g., π+π−) distributions as a baseline [41]; (3) a “hybrid method” between (1) and (2), as described in Refs. [41,42]); and (4) the three-particle cumulant method [43], which significantly suppresses the minijet related contributions and can be used as an alternative to the study of two-particle correlations. A method to suppress, in particular, minijet contributions in two-particle correlation functions was suggested in Ref. [44] and it is based on applying event-shape selections. It was shown that it is possible to differentiate between jetlike and spherical event topologies using a global characteristic of the event such the transverse sphericity [45,46] and the transverse spherocity [47,48]. It was observed for the first time in Ref. [44] that the pion radii for jetlike events are smaller than the source radii for spherical events. In jetlike events, the radii dependence on multiplicity is such that they increase with increasing kTin the lowest multiplicity interval and decrease with kTfor the highest multiplicities. There are no multiplicity dependences for these events. The radii for spherical events show an increase in system size with increasing multiplicity. They do not show any visible trend with kT, which differs from the results of sphericity-integrated (minimum-bias) pion and kaon analyses in Refs. [31,34], where the obtained radii decrease with increasing kT. This different behavior suggests [44] that the lower part of the transverse sphericity spectrum contributes to the observed slope in minimum bias (MB) pp collisions. In this work, the femtoscopic correlations of identical charged pions and kaons are investigated in pp collisions at √s=13 TeV. The purpose of this analysis is to study the transverse-momentum and multiplicity dependence of pion and kaon femtoscopic radii separately for jetlike and spherical events. The influence of the sphericity selections on the kaon femtoscopic radii is studied for the first time. The article is organized as follows. Section II briefly describes the ALICE experimental setup. Section III presents the event selection criteria. Section IV introduces the definition of sphericity and discusses the analysis methods to extract the femtoscopic correlation function for pion and kaon pairs and the estimation of the systematic uncertainties. The extracted femtoscopic parameters are shown and discussed in Sec. V. The results are summarized in Sec. VI. II. EXPERIMENTAL SETUP A detailed description of the ALICE detector and its performance can be found in Refs. [49,50]. In the present analysis, the information from the inner tracking system (ITS) [51], the time projection chamber (TPC) [52], the time-offlight (TOF) [53], and the V0 [54] detectors are used. The V0 detector is used for triggering on collision events. It is composed of two small-angle scintillator arrays, located at 340 and 90 cm from the nominal interaction point along the beam line and covering 2.8<η<5.1 (V0A) and −3.7< η<−1.7 (V0C), respectively. The events are selected with the MB trigger, which requires simultaneous signals in both parts of the V0 detector in coincidence with two beam bunches crossing in the ALICE interaction region. The rejection of 024915-2 FEMTOSCOPIC CORRELATIONS OF IDENTICAL … PHYSICAL REVIEW C 109, 024915 (2024) pile-up events is performed by using the vertexing capabilities of the silicon pixel detector (SPD) [50], which forms the two innermost layers of the ITS. Events with multiple vertices identified with the SPD (in-bunch pile-up) are removed from the analysis. Pile-up events from different bunch crossings are rejected by requiring the tracks to have hits in the SPD. The remaining leftover pile-up is negligible in the present analysis. Charged particles are reconstructed with the central barrel ITS and TPC detectors placed inside a solenoidal magnet providing a uniform 0.5 T field parallel to the beam direction. The primary vertex is reconstructed using the ITS. This detector is a silicon tracker with six layers of silicon sensors covering the pseudorapidity range |η|<0.9[51]. The TPC is the main tracking detector in ALICE, which measures the ionization energy loss of particles. The chamber is divided into two halves by a central electrode. The end caps on either side are composed of 18 sectors (covering the full azimuthal angle) with 159 pad rows placed radially in each sector. The TPC covers an acceptance of |η|<0.9 for tracks which reach the outer radius of the detector. Particle identification (PID) for reconstructed tracks is carried out using the TPC together with the TOF [53] detectors. The TOF is a cylindrical detector consisting of 18 azimuthal sectors divided into five modules along the beam axis with active element multigap resistive plate chambers. Pions and kaons were identified using the TPC and TOF detectors. The deviation of the specific energy loss (dE/dx) measured in the TPC from the one calculated using the Bethe-Bloch parametrization was required to be within a certain number of standard deviations (nσTPC ). A similar nσTOF method was applied for the particle identification in the TOF. The deviation is computed between the measured time of flight and the one calculated for a given particle path length, momentum, and mass. III. DATA SELECTION The data samples used in this work were recorded by ALICE in 2016–2018 during the LHC Run 2 period at √s= 13 TeV. After application of all selection criteria, about 109 minimum bias events were analyzed. Events were accepted if they had the collision vertex position measured along the beam line within ±10 cm from the nominal interaction point. The charged particle tracks were required to be reconstructed with the ITS and TPC detectors with a χ2per number of degrees of freedom (χ2/NDF) smaller than 4.0, and each track segment was reconstructed from at least 70 out of the 159 possible space points. The distance of closest approach (DCA) to the primary vertex was required to be smaller than 0.3 cm in both the transverse plane and the longitudinal direction. Femtoscopic correlation functions of identical particles are sensitive to two-track reconstruction effects because the particles of interest have close momenta and close trajectories. Two kinds of two-track effects, splitting and merging, were studied. The splitting of the tracks means that one track is reconstructed as two. The track merging means that two different tracks are reconstructed as one. To remove these effects, the distance between the tracks of two particles was calculated TABLE I. Charged pion selection criteria. Selection criterion Value pT0.15 <pT<4.0 GeV/c |η|<0.8 DCAtransverse <0.3cm DCAlongitudinal <0.3cm nσTPC <3 (for p<0.5 GeV/c) nσ2 TPC +n2 σTOF <3 (for 0.5<p<4.0 GeV/c) Number of track points in TPC ⩾70 at up to nine points throughout the TPC volume (every 20 cm, from 85 to 245 cm in the radial direction) and then averaged. It was required that the particles for each pair had an average TPC separation of at least 3 cm. Pions and kaons were selected in the pseudorapidity |η|< 0.8 range. For pions, the transverse momentum 0.15 <pT< 4.0GeV/crange was used. The pion selection criteria are presented in Table I. The pion purity is about 99% for track momenta p<2.0GeV/c, while, for the 2 <pT<4GeV/c interval, it decreases to 80% due to an increasing contamination from kaons. The selection criteria for the kaons are reported in Table II. In order to avoid strong contamination from pions, narrower momentum ranges were used for kaons, namely 0.15 <pT<1.5GeV/c. The dominant contamination for charged kaons is from e±in the particle momentum range 0.4<p<0.5GeV/c, resulting in a kaon purity of approximately 90%. Outside this range, the kaon purity is about 99%. IV. ANALYSIS TECHNIQUE Pions and kaons were selected in the same raw chargedparticle multiplicity intervals Ntrk of (1–18), (19–30), and (>30) in order to compare the obtained results in the same multiplicity conditions. The sphericity calculations (see Sec. IV A) require at least three tracks with pT>0.5GeV/c. Therefore, the lowest multiplicity interval is (1–18) if the sphericity calculation is not performed, while it is (3–18) when the sphericity is calculated. From now on, the lowest multiplicity interval will be denoted as (1–18) for both TABLE II. Charged kaon selection criteria. Selection criterion Value pT0.15 <pT<1.5 GeV/c |η|<0.8 DCAtransverse <0.3cm DCAlongitudinal <0.3cm nσTPC <2 (for 0.15 <p<0.4 GeV/c) <1 (for 0.4<p<0.45 GeV/c) <2 (for 0.45 <p<1.5 GeV/c) nσTOF <2 (for 0.5<p<0.8 GeV/c) <1.5 (for 0.8<p<1.0 GeV/c) <1.0 (for 1.0<p<1.5 GeV/c) Number of track points in TPC ⩾70 024915-3 S. ACHARYA et al. PHYSICAL REVIEW C 109, 024915 (2024) TABLE III. Raw charged-particle multiplicity (Ntrk) intervals and corresponding average dNch/dηcalculated from corrected multiplicity distributions in the |η|<0.8 range. The values are quoted with their systematic uncertainties, the statistical uncertainties are negligible. Ntrk dNch/dηST>0.7dNch/dηST<0.3dNch/dη 3(1)–18 7.8 ±0.4 6.2 ±0.3 5.1 ±0.2 19–30 15.0 ±0.7 13.5 ±0.6 14.3 ±0.7 >30 25.4 ±1.0 21.8 ±0.9 24.7 ±0.1 cases. The multiplicity for primary charged tracks [55]was estimated using the combined reference multiplicity estimator (SPD tracklets and tracks reconstructed in the ITS and the TPC) in the |η|<0.8 range. The SPD tracklets are track segments built by associating pairs of hits in the two SPD layers. For each raw multiplicity interval, the average chargedparticle pseudorapidity density dNch/dηwas obtained by converting the measured event multiplicities using Monte Carlo simulations with the PYTHIA 8.2 event generator [56] (with the Monash tune [57]) and the GEANT 3 package [58] for the transport of the generated particles through the ALICE detector. The intervals and their corresponding dNch/dη, for both cases with and without sphericity event selections (ST, defined in the next section), are shown in Table III. The systematic uncertainties for these densities were evaluated as the difference between their magnitudes when taking into account, or not, the detector efficiency correction using the Monte Carlo simulation mentioned above. The estimated value for these uncertainties is about 5%. A. Transverse sphericity In collider experiments, the study of the shape of the emitting source is often performed in the transverse x-yplane in order to avoid distortions related to the Lorentz boost in the beam direction along the zaxis [46]. Following this principle, the transverse sphericity (ST) was used to study event characteristics in pp collisions at the LHC by the ALICE Collaboration [45]. The transverse sphericity is defined as ST=2min(λ1,λ 2) λ1+λ2 ,(1) where λ1and λ2are the eigenvalues of the matrix of transverse particle momenta, ST=1 ipi T i 1 pi T⎛ ⎝pi x2pi xpi y pi xpi ypi y2⎞ ⎠,(2) with pi xand pi ybeing the components of the transverse momentum for ith particle  pi T. The transverse sphericity takes values in the (0–1) range. By definition of sphericity, in case of ST→0, the emitting source is a strongly elongated ellipse, while ST→1 corresponds to a nearly isotropic source in momentum or coordinate space. To ensure good resolution of the transverse sphericity calculation, only events with more than two primary tracks in |η|<0.8 and pT>0.5GeV/c were selected [45]. Following Ref. [44], ST>0.7 was used in FIG. 1. The experimental probability Pof having events of different transverse sphericity STin the given raw multiplicity Ntrk intervals (1–18), (19–30), and (>30). There are no corrections applied for the efficiency of the sphericity selection. Only statistical uncertainties are shown and are smaller than the marker size. this analysis to select spherical events. It is expected that, for these events, the multiple soft particle production processes dominates. For jetlike events with ST<0.3, hard processes such as jets and minijets become dominant. Figure 1shows the experimental probability of having events with different transverse sphericity for the given raw multiplicity intervals: (1–18), (19–30), and (>30). Sphericity is correlated with multiplicity, so the number of events with small STvalues is higher in the lowest multiplicity interval, while the larger multiplicity intervals contain more events with large sphericity values. The difference between spherical events, jetlike events, and events without sphericity selection can be clearly seen in Fig. 2, which presents the experimental and Monte Carlo distributions of the azimuthal angle difference ϕ between the trigger and the associated particles, where the trigger particle is the particle with the largest pTin the event, ptrig T>0.5 GeV/c,passoc T<ptrig T. All distributions are normalized by the number of associated particles: Nassoc(ST(0,1))=Nassoc(ST< 0.3) +Nassoc(ST>0.7) +Nassoc(ST(0.3,0.7)). The Monte Carlo simulations, with PYTHIA 8 as event generator and GEANT 3 for the simulation of the detector and the propagation of particles through the detector material, describe the ϕ distributions reasonably well for all sphericity selections. The jetlike events demonstrate a strong anisotropic structure. The peak at ϕ ≈0 corresponds to correlations within the jet determined by the trigger particle. The peak at ϕ →πcorresponds to the correlation of the particle associated with the jet moving in the opposite direction. Both peaks are absent for the sphericity selection ST>0.7. The ϕ distribution shows some specific features with respect to the distribution without sphericity selection, which are reasonably well described by PYTHIA 8. The spherical events are much 024915-4 FEMTOSCOPIC CORRELATIONS OF IDENTICAL … PHYSICAL REVIEW C 109, 024915 (2024) FIG. 2. The pion raw experimental distribution of the azimuthal angle difference ϕ between the trigger and the associated particles for ST>0.7 (red circles), ST<0.3 (blue squares), and ST(0,1) (green stars) compared with MC PYTHIA 8 calculations shown with the corresponding open markers. The calculations include particle transport through the ALICE detector using the GEANT 3 transport package. The statistical uncertainties are smaller than the marker size. more isotropic than the jetlike ones, and the jet structures are suppressed. B. Correlation functions The particle source created in hadronic or nuclear collisions is usually investigated using momentum correlations of two or more emitted particles. This analysis studies two-particle correlations. The observable of interest is the correlation function (CF) defined as C(p1,p2)=A(p1,p2)/B(p1,p2),(3) where A(p1,p2) is the two-particle momentum distribution in the given event, and B(p1,p2) is a reference distribution [59]. The former includes information on the source as well as on the FSI of the emitted hadrons and/or QS effects. The latter is constructed by mixing particles emitted in two different collisions to avoid any influence of pair correlation. In the present work, the reference distribution is constructed by mixing ten events with similar multiplicity and of close sphericities. It is also required that events in a mixed event pool have their vertex positions within 2 cm from each other along the beam direction. Due to the experimental limitation in the number of pairs, the CF is commonly defined in terms of a single kinematic variable instead of using the particle momentum vectors [see Eq. (3)]. In the following, the Lorentz-invariant qinv = √q2−q2 0is used, where q=p1−p2is the pair momentum difference and q0=E1−E2is the energy component difference. The measured correlation functions are corrected using the so called double-ratio technique for the MC simulated ones CMC(qinv). This procedure assumes that the signal and the background are factorized. The corrected correlation function can be written as Ccorr(qinv)=Cdata(qinv) CMC(qinv).(4) Generally, the CF includes several effects, such as femtoscopic effects (QS +Coulomb in the case of π±π±and K±K±correlations), minijet contributions at low qinv, and long-range correlations due to energy-momentum conservation at high qinv. The latter are present in the same-event pair relative-momentum distribution and absent in the mixed-event distribution determining the CFs. If spherical events are selected with ST>0.7, contributions of minijets are strongly suppressed. However, there is still influence of long-range correlations due to the conservation laws. Therefore, to correct the experimental CFs for these long-range effects in spherical events, a MC model which correctly describes the shape of the experimental CFs at large qinv are used. The experimental CFs can be divided by the MC ones [Eq. (4)], and the resulting CFs are considered to contain only femtoscopic effects, which can be fitted with a function including QS and Coulomb interaction. For ppcollisions at √s=13 TeV, the PYTHIA 8[56]MC model gives the best description of the experimental function outside the low qinv region. For jetlike (ST<0.3) events, there is a large contribution of minijets at low qinv in addition to the long-range correlations at high pair relative momentum. They can also be corrected using PYTHIA 8 calculations in order to consider femtoscopic correlations only. The analysis was performed separately for positively and negatively charged pions and kaons at two magnetic field polarities, after which the two-particle correlations were combined using their statistical uncertainties as weights. The analysis for pions and kaons was performed in the same three multiplicity intervals. For pions, five pair transverse momentum kTintervals were used: (0.15–0.3), (0.3–0.5), (0.5–0.7), (0.7–0.9), and (0.9–1.2) GeV/c.The analysis for kaons was performed in two kTintervals: (0.15– 0.5), (0.5–1.2) GeV/c. 1. Pion correlation functions Figure 3shows the pion experimental CF (green solid circles) for events with ST>0.7inpp collisions at √s= 13 TeV. The PYTHIA 8 (Monash) model calculations including the ALICE detector response were used to describe nonfemtoscopic effects and are also shown in the figure (blue crosses). All distributions are normalized to unity in the 0.7<qinv < 0.8GeV/crange, which is well outside the QS and Coulomb FSI region (qinv 0.4GeV/c) and before the noticeable large qinv slope associated with energy and momentum conservation. The CFs shown in Fig. 3are flat for the low multiplicity intervals in the region 0.5<qinv <1.0GeV/c.Forthetwo highest kTintervals, some slope of baseline appears. At qinv > 1.0GeV/c, the aforementioned kinematic effects are present especially for the lowest multiplicity intervals. The CFs decrease at qinv →0forthePYTHIA 8 calculations for the lowest multiplicity interval (Ntrk ⩽18) in the (0.5–0.7), (0.7–0.9), and (0.9–1.2) GeV/ck Tintervals. The occurrence of such minima is related to the three-tracks requirement, necessary for the transverse sphericity calculation [45]. Indeed, the number of available events with three tracks 024915-5 S. ACHARYA et al. PHYSICAL REVIEW C 109, 024915 (2024) FIG. 3. The π±π±experimental correlation functions (green solid circles) as function of the invariant pair relative momentum qinv in pp collisions at √s=13 TeV for the raw multiplicity Ntrk intervals of (1–18), (19–30), and (>30) in the (0.15–0.3), (0.3–0.5), (0.5–0.7), (0.7–0.9), and (0.9–1.2) GeV/ck Tintervals. A sphericity selection of ST>0.7 is applied. The data are compared with PYTHIA 8 calculations, shown by blue crosses. The error bars represent the statistical uncertainties, while the systematic uncertainties are negligible. with pT>0.5GeV/cdecreases at small qinv. Figure 4illustrates the pion experimental correlation function in pp collisions at √s=13 TeV compared with PYTHIA 8 model calculations for events with ST<0.3. The CFs for jetlike events shown in this figure exhibit a pronounced slope over the full qinv range, indicating the presence of nonfemtoscopic effects. These effects are especially pronounced for kT> 0.5GeV/c. As can be seen from the figure, the PYTHIA 8 FIG. 4. The π±π±experimental correlation functions (green solid circles) as function of the invariant pair relative momentum qinv in pp collisions at √s=13 TeV for the raw multiplicity Ntrk intervals of (1–18), (19–30), and (>30) in the (0.15–0.3), (0.3–0.5), (0.5–0.7), (0.7–0.9), and (0.9–1.2) GeV/ck Tintervals. A sphericity selection of ST<0.3 is applied. The data are compared with PYTHIA 8 calculations shown by blue crosses. The error bars represent the statistical uncertainties, while the systematic uncertainties are negligible. 024915-6 FEMTOSCOPIC CORRELATIONS OF IDENTICAL … PHYSICAL REVIEW C 109, 024915 (2024) FIG. 5. The K±K±experimental correlation functions (green solid circles) as function of the invariant pair relative momentum qinv in pp collisions at √s=13 TeV for the raw multiplicity Ntrk intervals of (1–18), (19–30), and (>30) in the (0.15–0.5) and (0.5–1.2) GeV/ck T intervals. A sphericity selection of ST>0.7 is applied. The data are compared with PYTHIA 8 calculations shown by blue crosses. The PYTHIA 8 calculations are approximated with a second-order polynomial (red curves). The error bars represent the statistical uncertainties, while the systematic uncertainties are negligible. model calculations describe reasonably well the pion experimental data for jetlike events at large qinv values. 2. Kaon correlation functions Figure 5shows the kaon experimental CF (green solid circles) for events with ST>0.7 and the corresponding PYTHIA 8 calculations (blue crosses) in pp collisions at √s=13 TeV. The strength of the charged kaon correlations, represented by the magnitude of C(qinv)forqinv →0, is smaller than observed for the pions and decrease with kT. The CFs for spherical events are flat at qinv >0.5GeV/cboth for the data and the MC calculations. The nonfemtoscopic background contributions obtained using PYTHIA 8werefittedwitha second-order polynomial, which then was used for the correction of the experimental CFs for nonfemtoscopic effects. The fit allows reducing the impact of statistical fluctuations on the extracted femtoscopic parameters. Figure 6presents the kaon experimental correlation function for events with ST<0.3 in pp collisions at √s=13 TeV, for the raw multiplicity intervals Ntrk of (1–18), (19–30), and (>30) in the (0.15–0.5) and (0.5–1.2) GeV/ck Tintervals. Similarly to the pion CFs for jetlike events (see Fig. 4), the kaon jetlike CFs shown in Fig. 6exhibit a pronounced slope at low qinv, indicating the presence of nonfemtoscopic effects. Such background is especially pronounced for kT>0.5GeV/c. As can be seen in the figure, the estimate of the femtoscopic signal with respect to the background effects in the highest Ntrk >30 multiplicity interval is not possible since the correlation functions coincide with PYTHIA 8 within statistical uncertainties. C. Correlation function parametrization In the previous analyses performed by the ALICE Collaboration in pp collisions, the Gaussian distribution of a particle source in the pair reference frame (PRF) was assumed for pions [31] and kaons [34]. In those cases, the fit was performed using the Bowler-Sinyukov formula [60,61] C(qinv)=N1−λ+λK(r,qinv)1+exp −R2 invq2 inv,(5) where Nis a normalization coefficient and K(r,qinv)isthe Coulomb function with a radius rdefined as K(r,qinv)=C(QS +Coulomb) C(QS) .(6) The parameters Rinv and λdescribe the size of the source and the correlation strength, respectively [see Eq. (5)]. The term C(QS) in Eq. (6) is a theoretical CF calculated with pure QS weights (wave function squared) and C(QS +Coulomb) corresponds to QS +Coulomb weights. However, since the pion CFs are strongly non-Gaussian due to the large resonance contribution, an exponential Bowler-Sinyukov function was used to fit the pion CF, as in Ref. [44]: C(qinv)=N{1−λ+λK(r,qinv) ×[1+exp (−Rinvqinv)]}D(qinv),(7) 024915-7 S. ACHARYA et al. PHYSICAL REVIEW C 109, 024915 (2024) FIG. 6. The K±K±experimental correlation functions (green solid circles) as function of the invariant pair relative momentum qinv in pp collisions at √s=13 TeV for the raw multiplicity Ntrk intervals of (1–18), (19–30), and (>30) in the (0.15–0.5) and (0.5–1.2) GeV/c kTintervals. A sphericity selection of ST<0.3 is applied. The data are compared with PYTHIA 8 calculations, shown by blue crosses and approximated with a second-order polynomial (red curves). The error bars represent the statistical uncertainties, while the systematic uncertainties are negligible. where D(qinv)=bqinv +1 accounts for the slope of the baseline which remains after the division by PYTHIA 8. The measured pion CFs shown in Figs. 3and 4were divided by the PYTHIA 8 baseline and fit with the exponential Bowler-Sinyukov formula of Eq. (7). Figure 7presents some examples of the pion CF fit with the Gaussian BowlerSinyukov formula of Eq. (5) (dotted line) and the exponential one of Eq. (7) (solid line). The exponential fit function describes the pion CF well for both spherical and jetlike events, although the description is not ideal for qinv <0.05 GeV/c. The kaon CFs for spherical and jetlike events were corrected using a second-order polynomial to describe the nonfemtoscopic background as explained above and fitted with the Gaussian Bowler-Sinyukov formula [Eq. (5)]. An example of such a fit is shown in Fig. 8for both spherical and jetlike events. 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Zurlo 135,56 024915-18 FEMTOSCOPIC CORRELATIONS OF IDENTICAL … PHYSICAL REVIEW C 109, 024915 (2024) (ALICE Collaboration) 1A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2AGH University of Krakow, Cracow, Poland 3Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine 4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India 5California Polytechnic State University, San Luis Obispo, California, USA 6Central China Normal University, Wuhan, China 7Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba 8Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico 9Chicago State University, Chicago, Illinois, USA 10China Institute of Atomic Energy, Beijing, China 11China University of Geosciences, Wuhan, China 12Chungbuk National University, Cheongju, Republic of Korea 13Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovak Republic 14COMSATS University Islamabad, Islamabad, Pakistan 15Creighton University, Omaha, Nebraska, USA 16Department of Physics, Aligarh Muslim University, Aligarh, India 17Department of Physics, Pusan National University, Pusan, Republic of Korea 18Department of Physics, Sejong University, Seoul, Republic of Korea 19Department of Physics, University of California, Berkeley, California, USA 20Department of Physics, University of Oslo, Oslo, Norway 21Department of Physics and Technology, University of Bergen, Bergen, Norway 22Dipartimento di Fisica, Università di Pavia, Pavia, Italy 23Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy 24Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy 25Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy 26Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy 27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy 28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy 29Dipartimento di Fisica “E. R. Caianiello” dell’Università and Gruppo Collegato INFN, Salerno, Italy 30Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy 31Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy 32Dipartimento Interateneo di Fisica “M. Merlin” and Sezione INFN, Bari, Italy 33European Organization for Nuclear Research (CERN), Geneva, Switzerland 34Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia 35Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway 36Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic 37Faculty of Physics, Sofia University, Sofia, Bulgaria 38Faculty of Science, P. J. Šafárik University, Košice, Slovak Republic 39Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 40Fudan University, Shanghai, China 41Gangneung-Wonju National University, Gangneung, Republic of Korea 42Department of Physics, Gauhati University, Guwahati, India 43Helmholtz-Institut für Strahlenund Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany 44Helsinki Institute of Physics (HIP), Helsinki, Finland 45High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico 46Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 47HUN-REN Wigner Research Centre for Physics, Budapest, Hungary 48Indian Institute of Technology Bombay (IIT), Mumbai, India 49Indian Institute of Technology Indore, Indore, India 50INFN, Laboratori Nazionali di Frascati, Frascati, Italy 51INFN, Sezione di Bari, Bari, Italy 52INFN, Sezione di Bologna, Bologna, Italy 53INFN, Sezione di Cagliari, Cagliari, Italy 54INFN, Sezione di Catania, Catania, Italy 55INFN, Sezione di Padova, Padova, Italy 56INFN, Sezione di Pavia, Pavia, Italy 57INFN, Sezione di Torino, Turin, Italy 024915-19 S. ACHARYA et al. PHYSICAL REVIEW C 109, 024915 (2024) 58INFN, Sezione di Trieste, Trieste, Italy 59Inha University, Incheon, Republic of Korea 60Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands 61Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovak Republic 62Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India 63Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 64Institute of Space Science (ISS), Bucharest, Romania 65Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 66Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico 67Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil 68Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico 69iThemba LABS, National Research Foundation, Somerset West, South Africa 70Jeonbuk National University, Jeonju, Republic of Korea 71Institut für Informatik, Fachbereich Informatik und Mathematik, Johann-Wolfgang-Goethe Universität Frankfurt, Frankfurt, Germany 72Korea Institute of Science and Technology Information, Daejeon, Republic of Korea 73KTO Karatay University, Konya, Turkey 74Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 75Lawrence Berkeley National Laboratory, Berkeley, California, USA 76Lund University Department of Physics, Division of Particle Physics, Lund, Sweden 77Nagasaki Institute of Applied Science, Nagasaki, Japan 78Nara Women’s University (NWU), Nara, Japan 79Department of Physics, School of Science, National and Kapodistrian University of Athens, Athens, Greece 80National Centre for Nuclear Research, Warsaw, Poland 81National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India 82National Nuclear Research Center, Baku, Azerbaijan 83National Research and Innovation Agency - BRIN, Jakarta, Indonesia 84Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 85Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands 86Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom 87Nuclear Physics Institute of the Czech Academy of Sciences, Husinecˇ Rež, Czech Republic 88Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA 89Ohio State University, Columbus, Ohio, USA 90Physics Department, Faculty of Science, University of Zagreb, Zagreb, Croatia 91Physics Department, Panjab University, Chandigarh, India 92Physics Department, University of Jammu, Jammu, India 93Physics Program and International Institute for Sustainability with Knotted Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan 94Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany 95Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 96Physik Department, Technische Universität München, Munich, Germany 97Politecnico di Bari and Sezione INFN, Bari, Italy 98Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 99Saga University, Saga, Japan 100Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India 101School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 102Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru 103Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria 104SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France 105Sungkyunkwan University, Suwon City, Republic of Korea 106Suranaree University of Technology, Nakhon Ratchasima, Thailand 107Technical University of Košice, Košice, Slovak Republic 108The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 109The University of Texas at Austin, Austin, Texas, USA 110Universidad Autónoma de Sinaloa, Culiacán, Mexico 111Universidade de São Paulo (USP), São Paulo, Brazil 112Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 113Universidade Federal do ABC, Santo Andre, Brazil 114Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Bucharest, Romania 115University of Cape Town, Cape Town, South Africa 024915-20 FEMTOSCOPIC CORRELATIONS OF IDENTICAL … PHYSICAL REVIEW C 109, 024915 (2024) 116University of Derby, Derby, United Kingdom 117University of Houston, Houston, Texas, USA 118University of Jyväskylä, Jyväskylä, Finland 119University of Kansas, Lawrence, Kansas, USA 120University of Liverpool, Liverpool, United Kingdom 121University of Science and Technology of China, Hefei, China 122University of South-Eastern Norway, Kongsberg, Norway 123University of Tennessee, Knoxville, Tennessee, USA 124University of the Witwatersrand, Johannesburg, South Africa 125University of Tokyo, Tokyo, Japan 126University of Tsukuba, Tsukuba, Japan 127Universität Münster, Institut für Kernphysik, Münster, Germany 128Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 129Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, Lyon, France 130Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France 131Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire (DPhN), Université Paris-Saclay, Saclay, France 132Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France 133Università degli Studi di Foggia, Foggia, Italy 134Università del Piemonte Orientale, Vercelli, Italy 135Università di Brescia, Brescia, Italy 136Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India 137Warsaw University of Technology, Warsaw, Poland 138Wayne State University, Detroit, Michigan, USA 139Yale University, New Haven, Connecticut, USA 140Yonsei University, Seoul, Republic of Korea 141Zentrum für Technologie und Transfer (ZTT), Worms, Germany 142Affiliated with an institute covered by a cooperation agreement with CERN 143Affiliated with an international laboratory covered by a cooperation agreement with CERN *Also at: Max-Planck-Institut fur Physik, Munich, Germany. †Also at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy. ‡Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy. §Deceased; Also at: An institution covered by a cooperation agreement with CERN. Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India. ¶Also at: Institute of Theoretical Physics, University of Wroclaw, Poland. 024915-21